Customer Ordered Without Required Fields

This site is running 1.3.9 and the checkout and registration are stock/original fields, no added or "extra fields" in checkout. Somehow, the site received an order recently without a Customer Name or Email - the basic fields in Create Account.

I am not sure how this is possible unless I am missing something I should toggle. The First Name and Last Name is set to a minimum of 2 characters for both.

The only thing slightly odd about this order is that it is for a product that is free (a product they already paid for offline) - so I am not sure if having the $0 product price and the free shipping are causing the person to be able to bypass those required fields?